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Mirrors > Home > ILE Home > Th. List > 0ss | Unicode version |
Description: The null set is a subset of any class. Part of Exercise 1 of [TakeutiZaring] p. 22. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
0ss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3372 |
. . 3
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2 | 1 | pm2.21i 636 |
. 2
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3 | 2 | ssriv 3106 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-dif 3078 df-in 3082 df-ss 3089 df-nul 3369 |
This theorem is referenced by: ss0b 3407 ssdifeq0 3450 sssnr 3688 ssprr 3691 uni0 3771 int0el 3809 0disj 3934 disjx0 3936 tr0 4045 0elpw 4096 exmidsssn 4133 fr0 4281 elnn 4527 rel0 4672 0ima 4907 fun0 5189 f0 5321 oaword1 6375 0domg 6739 nnnninf 7031 exmidfodomrlemim 7074 sum0 11189 ennnfonelemj0 11950 ennnfonelemkh 11961 0opn 12212 baspartn 12256 0cld 12320 ntr0 12342 bdeq0 13236 bj-omtrans 13325 el2oss1o 13359 nninfsellemsuc 13383 |
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